Block #222,767

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/22/2013, 11:11:05 AM · Difficulty 9.9396 · 6,590,075 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

ddeed4e8d96c667105c29dc8981e6864fa40d69d449fc59d6833355ed046ccde

View on Chainz ↗

Height

#222,767

Difficulty

9.939592

Transactions

Size

1.11 KB

Version

Bits

09f08918

Nonce

30,197

Timestamp

10/22/2013, 11:11:05 AM

Confirmations

6,590,075

Mined by

⛏️ fAbuU1HhSi58QcdzhwKqhpJiRG3JPwsJEbB

Merkle Root

a07bd50c36995e768dcb0bfe278ffb9243022587b829dc0adba22983591ed4bd

Transactions (3)

Coinbase0d1679d2089aaf…148292c62a3909

1 in → 1 out10.1300 XPM110 B

AbuU1HhS…JPwsJEbB

1b0933d573f283…a3b3e93e257d35

4 in → 6 out23.0704 XPM740 B

AQpsy9pD…aHseMfku AL7194fk…YNQBVjTB AT2w9AM1…YMN7C8VV AdToHhys…uNu3dqWo AbuU1HhS…JPwsJEbB

339d85f97bcf00…287fecb1532f69

1 in → 1 out3.0424 XPM193 B

AZekc9vM…TkyD7EeC

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

9.228 × 10⁹³(94-digit number)

92287903777557150630…12662686291191889919

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

9.228 × 10⁹³(94-digit number)

92287903777557150630…12662686291191889919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.228 × 10⁹³(94-digit number)

92287903777557150630…12662686291191889921

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.845 × 10⁹⁴(95-digit number)

18457580755511430126…25325372582383779839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.845 × 10⁹⁴(95-digit number)

18457580755511430126…25325372582383779841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

3.691 × 10⁹⁴(95-digit number)

36915161511022860252…50650745164767559679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.691 × 10⁹⁴(95-digit number)

36915161511022860252…50650745164767559681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

7.383 × 10⁹⁴(95-digit number)

73830323022045720504…01301490329535119359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.383 × 10⁹⁴(95-digit number)

73830323022045720504…01301490329535119361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.476 × 10⁹⁵(96-digit number)

14766064604409144100…02602980659070238719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.476 × 10⁹⁵(96-digit number)

14766064604409144100…02602980659070238721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #222,767

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